I don't think so. This looks like an empirical question -- what do you mean by "extremely hard"? Any evidence?

I don't know if anybody has ever studied this - I would be surprised if they had -, so I have only anecdotal evidence from the uncertainty I myself experience sometimes when choosing between "will", "going to", plain present, "will + progressive", and present progressive, and from the testimony of other highly advanced L2 speakers I've talked to who feel the same way - while native speakers are usually not even aware that there is an issue here.

She speaks better English (with some accent, to be sure) in the usual sense -- she has a rich vocabulary and doesn't make many mistakes.

How exactly is "rich vocabulary" not high-status? (Also, are you sure it actually contains more non-technical lexemes and not just higher-status lexemes?) I'm not exactly sure what you mean by "mistakes". Things that are ungrammatical in your idiolect of English?

While that is true, your claims weren't about averages. Your claims were about impossibility -- for anyone. An average person isn't successful at anything, including second languages.

I actually made two claims. The one was that it's not entirely clear that there aren't any such in-principle impossibilities, though I admit that the case for them isn't very strong. I will be very happy if you give me a reference surveying some research on this and saying that the empirical side is really settled and the linguists who still go on telling their students that it isn't are just not up-to-date.

The second is that in any case, only the most exceptional L2 learners can in practice expect to ever achieve native-like fluency.